颜色-卡西米尔邻接矩阵方法用于全重四夸克态
A Colour-Casimir Adjacency Matrix Approach to Fully-Heavy Tetraquarks
- Department of Physics, University of Kashan（卡尚大学物理系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出基于颜色-卡西米尔邻接矩阵的全重四夸克谱框架，用X(6900)、X(7100)、X(7200)标定参数，预测全底基态能量，并指出与实验的差异。
AI中文摘要：
我们提出了一个基于加权图谱谱理论的全重四夸克谱现象学框架。四个价夸克作为完全图$K_4$的顶点，边的权重由两个颜色单态二夸克-反二夸克通道（$\bar{3}\otimes3$和$6\otimes\bar{6}$）中的颜色-卡西米尔因子决定。物理态通过一个混合角描述为这些通道的相干混合。与早期基于拉普拉斯算子的版本不同，我们通过直接对角化颜色加权邻接矩阵来获得谱。我们解析地证明了这两种构造不等价，且拉普拉斯算子颠倒了颜色吸引与质量排序之间物理上预期的关系。利用$X(6900)$、$X(7100)$和暂定的$X(7200)$来确定混合角、能量标度和有效粲夸克质量，我们得到$\alpha=0.740$，$\gamma=23.2$ MeV，$m_c=1.77$ GeV。由于三个参数由三个输入固定，这种校准并非独立的统计检验。预测内容来自将相同参数应用于其他情况：全底基态被预测在18.7-18.9 GeV，而仅颜色模型对$T_{cc}^+$的束缚能约低93 MeV。这一差异为超出紧凑四部分子颜色图的远程分子动力学提供了定量指示。我们讨论了$X(7200)$的暂定性、与CMS径向激发解释的张力，以及没有自旋、轨道或衰变动力学的静态模型的局限性。
英文摘要：
We present a phenomenological framework for fully-heavy tetraquark spectroscopy based on spectral graph theory. The four valence partons are the vertices of \(K_4\), with edge weights fixed by the colour-Casimir factors of the two colour-singlet diquark--antidiquark channels, \(\bar3\otimes3\) and \(6\otimes\bar6\); a physical state is a coherent mixture of the two, controlled by one mixing angle. Unlike an earlier version, which passed the colour-weighted adjacency matrix through an absolute-degree graph Laplacian, here the spectrum is obtained by \emph{directly} diagonalising the adjacency matrix; we show analytically that the Laplacian step inverts the physical correspondence between colour attraction and mass ordering. Fixing the model's three parameters (mixing angle, energy scale, effective charm mass) against \(X(6900)\), \(X(7100)\), and the more tentative \(X(7200)\) gives \(α=0.740\), \(γ=23.2\,\mathrm{MeV}\), \(m_c=1.77\,\mathrm{GeV}\); with three parameters fixed by three inputs this has zero residual degrees of freedom and is not itself a statistical test. The framework's value rests instead on two genuinely predictive, zero-additional-parameter applications: the all-bottom ground state falls at \(18.7\)--\(18.9\,\mathrm{GeV}\) for standard \(m_b\), with no retuning; and for \(T_{cc}^+\) the same mechanism under-binds by \(\approx93\,\mathrm{MeV}\), a quantitative diagnostic of missing long-range (molecular) dynamics. We discuss the sensitivity to the tentative status of \(X(7200)\), the tension between this static colour-configuration picture and the diquark radial-excitation interpretation favoured by recent CMS data, and what further data would make the model falsifiable in a stronger sense.
